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On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

  • Feyzi Başar EMAIL logo and Hadi Roopaei
Published/Copyright: December 10, 2021
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Abstract

Let F denote the factorable matrix and X ∈ {p, c0, c, }. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (p(F), ), (p(F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

  1. (Communicated by Tomasz Natkaniec)

Acknowledgement

The authors would like to thank the referee for useful comments on the first version of this paper.

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Received: 2020-09-22
Accepted: 2021-01-05
Published Online: 2021-12-10
Published in Print: 2021-12-20

© 2021 Mathematical Institute Slovak Academy of Sciences

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